Apple's HomePod and HomePod Mini are fine WiFi speakers. I treated myself to two HomePod Minis to replace the old stereo. Unfortunately, the smart speakers connected as a stereo pair have a problem: whenever an update is due, they simply don't want to import it. Thankfully, there are ways to force HomePod and HomePod Mini to update.
1. Restart HomePod (Mini).
If the HomePod update does not want to install, you should first try to restart your HomePod. You should not use the Home app for this, but disconnect the device properly from the power supply. So pull the plug and wait about 10 seconds. You can then plug the HomePod or HomePod Mini back in. Once started, the update should run through.
2. Restart iPhone
Sometimes the HomePod's refusal to update is also related to the Home app on the iPhone: Restart your iPhone to rule out this source of error. The update may then run through.
3. Turn automatic updates off and on
You can also try whether the update blockade is related to the automatic update function: Open the Home app on iPhone, iPad or Mac and select the HomePod (Mini). Select "Home settings" by clicking on the house symbol: Here you will find the "Software updates" item. Turn off auto-updates for the HomePod(s) here, wait a few seconds, and turn them back on. Wait a little, the HomePod is usually up to date by the next day at the latest.
4. Ungroup the devices
Another reason for a stuck update can be the connection of two HomePods to a stereo pair: Here the Home app or the HomePods themselves sometimes seem to choke. So ungroup the devices via the Home app by clicking on the stereo pair in the Home app, tapping on "Ungroup devices" and waiting briefly. The HomePods are now addressed individually, which may help with the update.
5. Connect and reset HomePod to Mac
Whatever works: Unplug your HomePod and connect it to your Mac's USB-C port. It now appears in the Finder: You can now easily start the update here, just as you might know it from your iPhone or iPod, by clicking on "Restore HomePod". Attention: The HomePod will be reset to factory settings and you will have to set it up again!
Just wait and see
Of course, a missing HomePod update isn't the end of the world if everything works. Sometimes the HomePod (Mini) just takes a while to load the update. Since some HomePod updates offer significant functional improvements, it can make sense to update as soon as possible, especially if there are operational problems.